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FrobeniusNumber

FrobeniusNumber[{a1, ..., an}]
gives the Frobenius number of a1, ..., an.
  • The Frobenius number of a1, ..., an is the largest integer b for which the Frobenius equation a1x1+...+anxnEqualb has no non-negative integer solutions. The ai must be positive integers.
  • If the integers ai are not relatively prime, the result is Infinity.
  • If one of the ai is the integer 1, then the result is -1.
  • If b is the Frobenius number of a1, ..., an, then FrobeniusSolve[{a1, ..., an}, b] returns {}.
EXAMPLESCLOSE ALL
Basic Examples   (1)
The Frobenius number of 12, 16, 20, 27:
The Frobenius number of 12, 16, 20, 27:
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Applications   (2)
Make an array of Frobenius numbers:
Frobenius numbers of pairs:
Frobenius numbers of length-4 runs:
Properties & Relations   (1)
For a pair of relatively prime integers the Frobenius number has a closed form:
Check:
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